One of the inherent risks in flying an aircraft is a controlled flight into terrain (CFIT) incident. CFIT occurs when a flight impacts terrain while under positive control. Aside from incidents of suicide, this means the terrain impact came as a surprise to the pilot.

Controlled Flight Into Terrain Awareness is a special emphasis area in the Federal Aviation Administration's (FAA) practical test standards (PTS). The FAA felt it necessary to include this as a special emphasis area because of the prevalence of this type of incident.

3 Answers
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Get An Instrument Rating: Some CFIT accidents happen during a nasty mix of mountain flying, scud running and an inevitable flight into IMC, which ends with hitting the side of a mountain, an instrument rating here can be a truly valuable thing in these situations.

Plan Your Routes and Minimums Carefully: This takes place in the preflight and you should always check your charts for minimum altitudes as well as man made obstructions that may be in your flight path. Once you have your minimum altitude selected, stick to it. If weather does not permit that altitude either alter your course or scrub the flight. There is some good info from AOPA on it here.

Synthetic Vision: Apps like ForeFlight are quickly becoming common place in aviation as are glass cockpits, and these have proven invaluable in terms of terrain awareness and avoidance as many of them now include synthetic vision with terrain maps. Good preflighting is still key and you should always inform your self of all potential terrain before a flight, while technology can aid in avoidance you should always have a backup plan.

Avoid The Mountains: This is sometimes not an option but if you as the PIC feel uncomfortable you should always choose a route around terrain if possible.

Practice Mountain Flying: Just as you would with any other aspect of aviation you can always get an instructor and practice mountain flying. The FAA has some tips here but mountain flying carries its own risks and unique cases that you should be ready for. Mountains can have turbulent airflow and you should make an effort to understand how wind flows over them, you can find a discussion on it here.

Get a FIS-B Weather Receiver: As mentioned above winds can be important when flying. It's worth it to have an FIS-B weather in receiver so that you always have the most up to date information.

$\begingroup$+1 for the "practice mountain flying" bit (though I would phrase it as "Take a mountain flying class" personally) -- A lot of the mountain-related accidents probably don't qualify as "controlled" flight into terrain as you're arguably not in control if a downdraft slams you into a ridge, but being aware of the special challenges and dangers of mountain flying could help save your life if you're flying around in the mountains.$\endgroup$
– voretaq7Oct 15 '15 at 18:38

OK, so my rather flippant comment aside, avoiding controlled flight into terrain is largely an exercise in common sense (many FAA "Special Emphasis Areas" could be rolled up into a special emphasis on common sense).

It basically boils down to three things:

Knowing where the terrain / obstacles are.

Knowing where your aircraft is.

Ensuring your aircraft doesn't get too close to terrain or obstacles.

So how do we do that?

Charts and Elevation Figures

For many pilots there's a simple and practical way to do this printed right on your VFR sectional chart: The Maximum Elevation Figure (MEF):
The MEF indicates the tallest feature (terrain or obstacle) in a given quadrangle on the sectional. If you are flying with a healthy margin (500-1000 feet or more) between you and the Maximum Elevation Figure you will not hit terrain or obstacles - they will be below you.

The MEF is one reason charts expire: As new obstacles are constructed (buildings, radio towers, etc.) the MEF in each quadrangle will be updated appropriately.

ATC Information (and More Charts)

ATC deals with an altitude which is useful for all pilots to know: Minimum Instrument Altitude (MIA). This altitude provides a guaranteed obstacle/terrain clearance (1,000 feet, or 2,000 feet in designated mountainous areas) for instrument flights.

Operating at or above the Minimum Instrument Altitude for a region gives you similar protections to operating at or above the MEF altitude from the VFR sectional, and also usually ensures that ATC will have radar contact with you.

The Minimum Instrument Altitude (and another useful one, the Minimum Vectoring Altitude) are charted for center and TRACON facilities. Most pilots haven't ever seen these charts (they're "Not For Navigation" and not particularly useful unless you know the ground over which the sectors are drawn), but they are available from the FAA as supplemental information.

Aircraft Performance and Common Sense

Unfortunately some pilots don't have the option of flying over all the terrain they may have to deal with - pilots in mountainous areas have to use mountain passes to cross ridges, and may be flying between peaks that are above their altitude.

It's here that common sense and aircraft performance play into things: You know your aircraft has a given rate of climb given its current altitude and loading, and that terrain is rising at a given slope below you. It is then the pilot's responsibility to ensure that they can out-climb the terrain, and to ensure that there is an "out" (either another pass to divert to or enough room to safely make a 180-degree turn if the terrain is out-climbing the aircraft).

Fancy Electronic Tools

Electronic flight planning applications have made terrain avoidance much easier: programs like ForeFlight and Garmin Pilot include "Hazard Advisor" and "Altitude Advisor" functions that will show where your planned route will intersect terrain or obstacles.

Many electronic flight bag / flight planning programs also include limited synthetic vision capabilities, and some glass-cockpit aircraft also include these capabilities. The virtual terrain presentation available using synthetic vision systems can be helpful if flying in IMC or marginal VFR weather:

$\begingroup$I know nothing about piloting but 500 ft seems like an awfully small amount of clearance. Can it really be that low? I expected more like 2,000 feet...$\endgroup$
– user541686Oct 15 '15 at 23:31

$\begingroup$@Mehrdad Per FAR 91.119 500 feet AGL / 500 feet from any "person, vessel, vehicle, or structure"is the absolute bare minimum for an airplane (in wide-open or sparsely-populated areas), and 1000 feet is the minimum for "congested areas". 2000 feet is a much more practical number though.$\endgroup$
– voretaq7Oct 16 '15 at 3:02

$\begingroup$You might want to mention the OROCA as well, unlike the MEF it includes vertical clearance from terrain and obstacles. It's shown on the regular IFR en route charts.$\endgroup$
– PondlifeOct 16 '15 at 7:12

The most important thing for the safety of any flight happens before you leave the ground, and that is planning. Know your route, have contingencies, and set limits on deviations. Set conditions on when you will abandon your plans and turn back, and stick to them regardless of peer pressure. Try making a good decision while you're being bounced around in turbulence, the visibility is rapidly worsening, and you have a bunch of people who know nothing about flying telling you to just go for it and you'll see why it is better to have a plan.

Many CFIT accidents happen because pilots fly into poor weather and elect to go on rather than turn back, which is sometimes called get-there-itis. You've flown 2 hours and the destination is only 30 minutes ahead, surely this cloud bank is only a mile or two thick and I'm instrument rated. Oops - where'd that mountain come from?! Flying through clouds is not safe without planning, even if with an instrument rating.

Other accidents happen because pilots decide to fly below weather. The weather keeps getting lower so they go lower until they are too low to avoid terrain. They didn't set a limit on how low the weather has to get before they turn back, or if they set a limit they don't stick to it because of wishful thinking or get-there-itis.

All the fancy tools in the world are no substitute for a map and good planning.